Falling liquid films
- London ; New York : Springer, c2012.
- Physical description
- xv, 440 p. : ill. ; 25 cm.
- Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 176.
QC176.83 .F35 2012
- Unknown QC176.83 .F35 2012
- Includes bibliographical references and index.
- Preface. -Acknowledgements. -Nomenclature. -Introduction. -Review of Phenomenology. -Modelling: state-of-the-art. -Structure of the book. -1 Flow and heat transfer. -1.1 Governing equations and boundary conditions. -1.2 Dimensionless equations, scalings and parameters. -1.3 The role of the Biot number. -1.4 Salient features. -1.5 References and further reading. -2 Primary instability. -2.1 Linear stability analysis. -2.2 Transverse disturbances. -2.3 Longtitudinal disturbances. -2.4 Mechanism of the hydrodynamic instability. -2.5 Salient features. -2.6 References and further reading. -3 Boundary layer-like approximation. -3.1 Boundary layer equations. -3.2 2D Boundary Layer Equations. -3.3 Strong surface tension limit. -3.4 Shkadov's scaling. -3.5 Reduction of the governing equations. -3.7 Scalings: three sets of parameters. -3.8 Salient features. -3.9 References and further reading. -3.10 Appendix. -4 Methodologies for flows at low Re. -4.1 Long-wave asymptotic expansion. -4.2 Validity domain of the Benney equation. -4.3 Parametic study for closed and open flows. -4.4 Regularization a la Pade. -4.5 Comparison of the different one-equation models. -4.6 Weakly nonlinear models. -4.7 Salient features. -4.8 References and further reading. -4.9 Appendix. -4.10 Physical parameters. -4.11 Small Biot number, analogy with forced convection. -5 Methodologies for moderate Re. -5.1 Averaged two-equation models. -5.2 Relaxing the self-similar assumption. -5.3 Methods of weighted residuals. -5.4 First-order formulation. -5.5 Comparison of methods of weighted residuals. -5.6 Second-order formulation -5.7 Reduction of the full second order model. -5.8 Salient features. -5.9 References and further reading. -6 Isothermal case: 2D flow. -6.1 Linear stability analysis. -6.2 Travelling waves. -6.3 Spatial evolution of 2D waves. -6.4 Salient features. -6.5 References and further reading. -6.6 Appendix. -7 Isothermal case: 3D flow. -7.1 Phenomenology. -7.2 2D modelling of 3D film flows. -7.3 Floquet Analysis: 3D stability of 2D waves. -7.4 2D simulations of 3D flows. -7.5 Salient features. -7.6 References and further reading. -7.7 Appendix. -8 Interaction of 3D solitary waves. -8.1 A model system for low-dimensional complexity. -8.2 Speed of 3D solitary pulses. -8.4 Approximate analytical solution. -8.5 Coherent structures theory. -8.6 Salient features. -8.7 References and further reading. -9 Heated films. -9.1 Formulation. -9.2 Formulation at first order. -9.3 Reduced models. -9.4 Regularized model. -9.5 Linear stability results. -9.6 Solitary waves. -9.7 Refined models. -9.8 Three-dimensional wave patterns. -9.9 Salient features. -9.10 References and further reading. -9.11 Appendix. -10 Reactive falling films. -10.1 Problem definition and governing equations. -10.2 Long-wave theory. -10.3 Kapita-Shkadov model and weighted residuals. -10.4 Salient features. -10.5 References and further reading. -10.6 Appendix. -11 Outlooks. -11.1 What has been offered/achieved. -11.2 Open questions - Suggestions. -11.3 References and further reading. -Conclusions. -Bibliography. -Index. -Summary.
- (source: Nielsen Book Data)
- Publisher's Summary
- This research monograph gives a detailed review of the state-of-the-art theoretical methodologies for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar, inclined substrate. This prototype is an open-flow hydrodynamic instability representing an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. Whenever possible, the link between theory and experiments is illustrated and the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of the underlying basic physics. It will be of benefit to a variety of readers, including advanced graduate students interested in interfacial fluid mechanics, researchers working on the theoretical and experimental aspects of thin film flows, and engineers whose work involves thin films, either isothermal or heated.
(source: Nielsen Book Data)
- Publication date
- S. Kalliadasis, C. Ruyer-Quil, B. Scheid, M.G. Velarde.
- Applied mathematical sciences, 0066-5452 ; v.176